The 28-year-old star met Miley, 21, on a trip to Los Angeles after chatting with her on Twitter and is self-confessed fan.
Lily insists the satirical video for her comeback single 'Hard Out Here' wasn't an attack against the 'Wrecking Ball' hitmaker, despite it showing her surrounded by twerking scantily-clad dancers.
Lily, 28, the Daily Mirror newspaper: ''I'd never met her before so I couldn't say we are really great friends but I do really like Miley.
''She's funny, witty and clever, I love what she does. I think her and Lorde's album have had the most plays in my car this year. I never went on record saying the video was a direct pop at her - it wasn't.
''She's probably way too busy for someone like me but yeah, I'd welcome the opportunity to work with her.''
Lily also insisted she doesn't feel the need to explain her 'Hard Out Here' video, which as well as being interpreted as an attack against Miley has been branded racist and sexist by some commentators because of its content.
She said: ''People have come up with so many conclusions about that video that if I had to explain each of them I'd be there for hours. So I didn't feel the need to explain anything to her (Miley) when it came out.
''Anyone who knows me, or follows me on Twitter, knows I love that girl more than anything.''
Steven Tyler prays for Chris Cornell during Asia show.
'Pirates of the Caribbean' is an exciting new career development for Brenton Thwaites.
The actor didn't want to be "wolfy".
Tragedy strikes in Manchester